Fractionally Spaced Equalization of Nonlinear Channels

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Fractionally Spaced Equalization (FSE) has become the focus of much research attention since the discovery that fractionally sampling the output of a channel permits its identification from the second-order statistics of the channel output under generically satisfied conditions. Blind schemes in turn are desirable in fading multipath environments where frequent changes in the channel dynamics, makes training signals very wasteful. Most of the blind Fractionally Spaced Equalization literature has been devoted to linear channels. Yet many channels such as satellite and microwave channels with nonlinear amplifiers, underwater and magnetic recording channels are inherently nonlinear. This is particularly so if the amplifiers operate in their most power efficient regimes. Further, in fiber optical communications, having an abundant bandwidth, the greatest challenge, is posed by dispersive nonlinearities in the channel. In many such instances blind equalization is natural and it is important to consider blind FSE of nonlinear channels.This study concerns the blind Fractionally Spaced Equalization of FIR channels characterized by a baseband channel output that is a polynomial function of the current and past values of the input. The equalizers sought also belong to this class. Using the concept of coprimeness of nonlinear systems, and employing difference algebraic techniques, a fundamental investigation into the equalization of this class of channels is being conducted. Conditions under which these channels are equalizable, and can be identified by the second order statistics of the output are being explored. Statistical and deterministic methods are employed. Direct and indirect equalizer design methodologies are formulated. Zero Forcing and Minimum Mean Squared Error equalizers are designed. Subspace methods are used. Adaptive schemes are postulated. Fundamental existence issues as well practical design issues are considered.